Surface profilometers, such as interferometric microscopes, have become a basic metrology tool for the characterization of high quality optical surfaces with sub-Angstrom rms roughness. For the last few decades, the standard list of output parameters of an interferometric microscope measurement included values of roughness averaged over an area and along a sample line. This was extended to a more rigorous statistical description of the surface topography based on power spectral density (PSD) distributions of the surface height. For example, the measured PSD distributions provide a basis for sophisticated calculations of three-dimensional scattering of x-rays by the optics.
A straightforward transformation of the measured 2D area distribution of the residual surface heights into a 2D PSD distribution always provides spectra with distortion caused by the unknown spatial frequency response of the instrument. The response is characterized by the modulation transfer function (MTF), determining the bandwidth of the instrument. The MTF contains contributions from the instrumental optical system, detector, signal processing, software algorithm, and environmental factors. Generally, these contributions are difficult to account for separately.
The task of designing high performance X-ray optical systems requires the development of sophisticated X-ray scattering calculations based on rigorous information about the optics. One of the most insightful approaches to these calculations is based on the power spectral density (PSD) distribution of the surface height. The major problem of measurement of a PSD distribution with an interferometric and/or atomic force microscope arises due to the unknown Modulation Transfer Function (MTF) of the instruments. The MTF characterizes the perturbation of the PSD distribution at higher spatial frequencies.